On the growth rate for three-layer HeleShaw flows: Variable and constant viscosity cases
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The linear stability of three-layer Hele-Shaw flows with middle-layer having variable viscosity is considered. Based on application of the Gerschgorin's theorem on finite-difference approximation of the linearized disturbance equations, an upper bound of the growth rate is given and its limiting case for the case of constant viscosity middle-layer is considered. A weak formulation of this equation, we obtained after some analysis. The upper bound in this case has also been derived here by analyzing an weak formulation of the problem. 2005 Elsevier Ltd. All rights reserved.
International Journal of Engineering Science
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